Related papers: Uniform projection designs under the stratified $L…
This paper develops a unified framework for partial identification and inference in stratified experiments with attrition, accommodating both equal and heterogeneous treatment shares across strata. For equal-share designs, we apply recent…
Points in the unit cube with low discrepancy can be constructed using algebra or, more recently, by direct computational optimization of a criterion. The usual $L_\infty$ star discrepancy is a poor criterion for this because it is…
We consider random discrepancy under weighted importance sampling of a class of stratified input. We give the expected $L_p-$discrepancy($2\leq p<\infty$) upper bound in weighted form under a class of stratified sampling. This result…
We consider the minimum distance projection in the $L_2$-norm from an arbitrary point in an $n$-dimensional, Euclidian space onto the canonical simplex. It is shown that this problem reduces to a univariate problem that can be solved by a…
We extend the notion of jittered sampling to arbitrary partitions and study the discrepancy of the related point sets. Let $\mathbf{\Omega}=(\Omega_1,\ldots,\Omega_N)$ be a partition of $[0,1]^d$ and let the $i$th point in $\mathcal{P}$ be…
The construction of uniform designs (UDs) has received much attention in computer experiments over the past decades, but most of the previous works obtain uniform designs over a U-type by lattice domain. Due to increasing demands for…
The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched…
This paper considers the problem of design-based inference for the average treatment effect in finely stratified experiments. Here, by "design-based'' we mean that the only source of uncertainty stems from the randomness in treatment…
Stratifying systems, which have been defined for module, triangulated and exact categories previously, were developed to produce examples of standardly stratified algebras. A stratifying system $\Phi$ is a finite set of objects satisfying…
Experimental designs intended to match arbitrary target distributions are typically constructed via a variable transformation of a uniform experimental design. The inverse distribution function is one such transformation. The discrepancy is…
In this article we obtain uniform effective upper bounds for the projective dimension and the Castelnuovo-Mumford regularity of homogeneous ideals inside a standard graded polynomial ring $S$ over a field. Such bounds are independent of the…
Popularly used eigendecomposition-based criteria such as BIC type, ratio estimation and principal component-based criterion often underdetermine model dimensionality for regressions or the number of factors for factor models. This…
Consider a stratified space with a positive Ricci lower bound on the regular set and no cone angle larger than 2$\pi$. For such stratified space we know that the first non-zero eigenvalue of the Laplacian is larger than or equal to the…
Follow-up experimental designs are popularly used in industry. In many follow-up designs, some additional factors with two or three levels may be added in the follow-up stage since they are quite important but may be neglected in the first…
The uniform position principle states that, given an irreducible nondegenerate curve C in the projective r-space $P^r$, a general (r-2)-plane L is uniform, that is, projection from L induces a rational map from C to $P^1$ whose monodromy…
We consider the problem of reconstructing binary images from their horizontal and vertical projections. It is known that the projections do not necessarily determine the image uniquely. In a previous paper it was shown that the symmetric…
Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…
We investigate the uniform approximation provided by least squares polynomials on the unit Euclidean sphere $\mathbb{S}^q$ in $\mathbb{R}^{q+1}$, with $q\ge 2$. Like any other polynomial projection, the study concerns the growth, as the…
One can associate to a complex projective structure on a surface holomorphic quadratic differential $\Phi$ via the Schwarzian derivative and a bending lamination $\lambda$ via the Thurston parameterization. In this note we obtain upper…
The method of stable random projections is popular for efficiently computing the Lp distances in high dimension (where 0<p<=2), using small space. Because it adopts nonadaptive linear projections, this method is naturally suitable when the…